Plastic pipes of the above-described type with integrated coupling, i.e., with coupling parts rigidly or integrally attached to the pipe ends, usually must be provided with at least one pipe end part having a recess serving to receive a sealing ring. However, it is particularly advantageous to provide both pipe and parts with recesses. In such an arrangement the recess on one pipe end part has stepped shoulders such that the lower part of the recess acts as a support for the sealing ring and the part of the recess of smaller thickness extends on both sides of the support and is overlapped by the coupling sleeve which extends away from the other pipe end part of the adjacent pipe. The coupling sleeve is fixed in a recess of the other pipe end part. Contrary to the first case, in which the coupling sleeve extends beyond the external diameter of the pipe, the coupling described in the second case has the same external diameter as the coupled pipe. However, it has been common practice hitherto in either case to produce the recesses needed on the pipe end parts by grinding off an external wall layer after completion of the pipe. This is disadvantageous due to the associated amount of labor and the wear of the pipe material, and also the fact that the homogeneous course of the layers of the multilayer pipe wall is thereby interrupted. This is particularly disadvantageous if glass fiber-reinforced layers are also touched or completely removed by the grinding. This happens especially in the case of the relatively deep recess used to receive an ordinary sealing ring.